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frank0520
 one year ago
Let F be the vector field F=(13x^2 y+3y^3 y)i 12x^3 j. Find the maximum value of
∫F•dr where c is positively oriented simple closed curve.
frank0520
 one year ago
Let F be the vector field F=(13x^2 y+3y^3 y)i 12x^3 j. Find the maximum value of ∫F•dr where c is positively oriented simple closed curve.

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ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1You may start with green's thm I think

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\[\oint F.dr = \iint\limits_{R} \text{curl}(F)~dA = \iint\limits_{R} 49x^29y^2+1~dA \]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Easy to see that the integrand stays positive in the region \(49x^2+9y^2 \lt 1\), so should we pick this as region of integration ?

frank0520
 one year ago
Best ResponseYou've already chosen the best response.1Here is a picture of the question.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Then we're correct, go ahead and evaluate the integral over that ellipse

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\[max(\oint F.dr) ~= ~\iint\limits_{49x^2+9y^2\lt 1}~~149x^29y^2~dA\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1you will need to use change of variables

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1I'm getting \(\dfrac{21\pi}{2}\) http://www.wolframalpha.com/input/?i=21*%5Cint_0%5E%282pi%29%5Cint_0%5E1+%281r%5E2%29*r+dr+d%5Ctheta

frank0520
 one year ago
Best ResponseYou've already chosen the best response.1looks correct to me, I got \[\frac{ 42\pi }{ 4 }\]
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